Atletico took a seventh-minute lead through Diego Forlan only for Sergio Ramos to level with a header in the 14th as Real dominated in an electric atmosphere at the Bernabeu.
Cristiano Ronaldo put the hosts ahead in the 61st and just when Atletico looked like they might have weathered the storm their defenders gifted Real a third in the 90th.
Luis Felipe stuck out a leg to divert the ball to unsuspecting teammate Alvaro Dominguez who stumbled backwards allowing it to run between his legs, and Ozil stepped in to score past a motionless David de Gea.
Earlier, Almeria put their poor league form behind them to beat Deportivo Coruna 1-0 at home after Knut Rindaroy deflected a low cross into his own net after 34 minutes.
Although the hosts dominated they failed to build on their lead and the visitors struck the post through Lassad in the second half.
On Wednesday, Barcelona thrashed second division Real Betis 5-0 at the Nou Camp and holders Sevilla came back to draw 3-3 at Villarreal. The second legs of all four matches are next week.
